#define _CRT_SECURE_NO_WARNINGS
#include<vector>
#include<string>
using namespace std;
int minInsertions(string s) {
    int n = s.size();
    vector<vector<int>> dp(n, vector<int>(n));
    for (int i = n - 1; i >= 0; i--) {
        dp[i][i] = 0;
        for (int j = i + 1; j <= n - 1; j++) {
            if (s[i] == s[j]) {
                if (i + 1 == j)dp[i][j] = 0;
                else dp[i][j] = dp[i + 1][j - 1];
            }
            else {
                dp[i][j] = min(dp[i][j - 1], dp[i + 1][j]) + 1;
            }
        }
    }
    return dp[0][n - 1];
}